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This is really a power distribution question, probably specific to the UK... Why is it some 11kv overhead lines have 3 conductors (cables) and some have 2? I have seen pole mounted transformers (PMTs) being fed by 3 conductors and some PMTs being fed by 2, is it possible to have a PMT that functions using only 1 feed!? (I've never seen any!)
What is going on inside a PMT that it seems to need at least 2 feeds? and do the ones with 3 lines feeding into them deliver more voltage/current/power? or is it the same as 2?

I am not a power engineer but a 3-wire 11 kV transmission line crosses my property and from which we receive two 240-volt 2-phase supplies.

40-years long past we had a single phase "nominal" 230-V supply from a pitifully small pole-mounted transformer some 200 yards away which in fact delivered 180-volts if more than one electric kettle was energised

That transformer was connected by two wires from a 11-kvolt feeder which came cross country on poles - i.e. the transformer was connected across two phases.I prefer not to remember the horrific problems I had in providing practical earthing particularly because we sit on several hundred feet of slate with the overburden ranging between 1-inch and possibly as much as 20-inches!

It took me well over a year to convIince the then SWEB - and their chief engineer - that it simply would not stand up to my installation of some 220-kwatts of equipment. Finally they extended the three wire feeder to a large tansformer on this property from which they supplied me with a single 240-volt supply rated 100 amps

(En passant I will relate that they failed to change my meter and at the following bank holiday Monday we had a meter that was threatening to go into orbit blanketed by a thick pall of black smoke - I had to threaten legal proceedings before it was hurriedly rectified.)

Some months later the adjacent Slate works jumped onto my bandwagon and the full11kV feeder was extended thus allowing them to install 3-phase cutting machinery. At the same time I hammered the table and pointed out that our transformer had a centre-tapped secondary and thus, without any expense, they could provide me with 2 x 100A feeds.

It would seem that your confusion over three-phase supplies is not unique? However, just to make confusion even more confused the supply to my house comes overhead via a single-core (co-ax) armoured cable with the armouring serving as (a) anti-varmint (b) neutral and (c) the company Earth. II did a lot of head scratching when it came to installing RCD's but my installation has proved safe and easy to seek out faults for the last 40 years. I wish I could be so certain since necessity arose to call in local electricians who have "corrected" my mistakes!

For all mYy passage into age-related incompetence I was on hand to point up a real danger which showed that my daughter's music room has been provided with 2 x 240-supplies in anti-phase! ! The entire arrangement offers plenty of scope for such errors when I installed a sewage pump and ran an alarm circuit into the house!

The line is feeding a three-phase transformer with a three-phase LV load (or three, single phase loads)

"And some have 2"
In this case the line is feeding a single or split phase transformer

"is it possible to have a PMT that functions using only 1 feed!? (I've never seen any!) "
Yes, but not in Britain. It is seen in rural Australia and is called Single Wire Earth Return (SWER)

"What is going on inside a PMT that it seems to need at least 2 feeds?"
It is using the two HV phase conductors as a closed circuit (kirchoffs law - what goes in, must come out).
If the transformer LV is single phase you will get the LV neutral tapped at the end of the LV winding and the phase at the other, so, therefore 230V phase-neutral.

If the transformer LV is split phase and centre tapped, you will get 230V phase-neutral and 460V phase-phase with the phases being 180° apart (or more likely in an older installation, 245V phase-neutral and 490V phase-phase).

"3 lines feeding into them deliver more voltage/current/power?"
Yes, three phases will give up to half as much power again as two phases

It comes down to cost. Unless the consumer needs the power, it is obviously cheaper to run two conductors rather than three (and in Australia, where the distances are enormous, it is cheapest to run just one conductor).

In my remote youth a device which took its feed froma 230-volt single phase and produced a three-phase output; it was packed in a ventilated (perforated steel) cabinet filled with an assortment of Transformers and chokes that would have done credit to HM Navy.

Apart from the fact that it worked I have no idea just how. Can anybody enlighten me please.

An electric circuit needs at least two conductors (plus often a protective earth) These are usually wires or cables, though exceptionly the mass of earth is used as one conductor.

A 2 wire 11KV overhead line would be single phase, and therefore only single phase loads can be served.
The step down transformers could in principle be made with any desired voltage output, but in practice in the UK the output will be either 230* volts, or 460* volts with an earthed center tap so as to give two 230* volt circuits.

A 3 wire 11kv overhead line will be 3 phase, and can supply either single phase loads at 230* or 230*/460* volts as described above, or can supply 3 phase at 230*/400* volts.

*all voltages are nominal or declared voltages, the actual voltages at the transformer are typicly about 250/500 volts for single phase, and about 250/433 volts three phase.

In years gone by, three phase motors could be worked from a single phase supply by means of a "phase converter" these consisted of a tapped transformer and a large capacitor to produce "fake" 3 phase to drive a motor. The motor inductance was a part of the circuit, that is the converter would not drive a 3 phase bank of lamps.

When I was at sea (up until 2002), I often used to call into Pusan in South Korea. Taking the bus from the container terminal into the city, we regularly passed a road where there was a single overhead line supported on a solitary HV insulator on top of the poles. The distribution network utilised an earth return. Due to the impedance of the earth return being somewhat greater than copper or aluminium, this gave an interesting LV supply voltage depending on load and weather; confirmed by the fact that in every bar, a variable voltage transformer could be seen as "standard equipment"!

For that matter, in northern America, you often see poles with a 3-wire HV supply at the top, and LV distribution cables below. The transformers usually appear to be three separate single-phase transformers, each with a single HV insulator. This implies that each transformer is connected between a HV phase and earth - since the three transformer "cans" are commoned, the earth connection only has to carry the out-of-balance current (assuming the simple case and no harmonics).

For interests sake, note that for a single phase HV/LV transformer connected across two 11 kV phases (such as in the UK) that due to capacitance between the HV windings and the transformer casing, there will be an earth current - alternatively, if the HV earth connection is cut, then the voltage between the transformer casing and earth will be considerable.